Melvyn Bragg and his guests discuss Einstein’s theories of relativity. Between 1905 and 1917 Albert Einstein formulated a theoretical framework which transformed our understanding of the Universe. The twin theories of Special and General Relativity offered insights into the nature of space, time and gravitation which changed the face of modern science. Relativity resolved apparent contradictions in physics and also predicted several new phenomena, including black holes. It’s regarded today as one of the greatest intellectual achievements of the twentieth century, and had an impact far beyond the world of science.

With:
Ruth Gregory
Professor of Mathematics and Physics at Durham University

Martin Rees
Astronomer Royal and Emeritus Professor of Cosmology and Astrophysics at the University of Cambridge

Roger Penrose
Emeritus Rouse Ball Professor of Mathematics at the University of Oxford.

Melvyn Bragg and his guests discuss the evolution of the Scientific Method, the systematic and analytical approach to scientific thought.

In 1620 the great philosopher and scientist Francis Bacon published the Novum Organum, a work outlining a new system of thought which he believed should inform all enquiry into the laws of nature. Philosophers before him had given their attention to the reasoning that underlies scientific enquiry; but Bacon’s emphasis on observation and experience is often seen today as giving rise to a new phenomenon: the scientific method.

The scientific method, and the logical processes on which it is based, became a topic of intense debate in the seventeenth century, and thinkers including Isaac Newton, Thomas Huxley and Karl Popper all made important contributions. Some of the greatest discoveries of the modern age were informed by their work, although even today the term ‘scientific method’ remains difficult to define.

With:
Simon Schaffer
Professor of the History of Science at the University of Cambridge

John Worrall
Professor of the Philosophy of Science at the London School of Economics and Political Science

Michela Massimi
Senior Lecturer in the Philosophy of Science at University College London.

Logic, the study of reasoning and argument, first became a serious area of study in the 4th century BC through the work of Aristotle. He created a formal logical system, based on a type of argument called a syllogism, which remained in use for over two thousand years.

In the nineteenth century the German philosopher and mathematician Gottlob Frege revolutionised logic, turning it into a discipline much like mathematics and capable of dealing with expressing and analysing nuanced arguments. His discoveries influenced the greatest mathematicians and philosophers of the twentieth century and considerably aided the development of the electronic computer. Today logic is a subtle system with applications in fields as diverse as mathematics, philosophy, linguistics and artificial intelligence.

With:
A.C. Grayling
Professor of Philosophy at Birkbeck, University of London

Peter Millican
Gilbert Ryle Fellow in Philosophy at Hertford College at the University of Oxford

Rosanna Keefe
Senior Lecturer in Philosophy at the University of Sheffield.

Melvyn Bragg discusses the epic feud between Sir Isaac Newton and Gottfried Leibniz over who invented an astonishingly powerful new mathematical tool – calculus. Both claimed to have conceived it independently, but the argument soon descended into a bitter battle over priority, plagiarism and philosophy.

Set against the backdrop of the Hanoverian succession to the English throne and the formation of the Royal Society, the fight pitted England against Europe, geometric notation against algebra. It was fundamental to the grounding of a mathematical system which is one of the keys to the modern world, allowing us to do everything from predicting the pressure building behind a dam to tracking the position of a space shuttle.

Melvyn is joined by Simon Schaffer, Professor of History of Science at the University of Cambridge and Fellow of Darwin College; Patricia Fara, Senior Tutor at Clare College, University of Cambridge; and Jackie Stedall, Departmental Lecturer in History of Mathematics at the University of Oxford.

The Logical Positivists argued that much previous philosophy was built on very shaky foundations, and they wanted to go right back to the drawing board. They insisted that philosophy – and science – had to be much more rigorous before it started making grand claims about the world.

The movement began with the Vienna Circle, a group of philosophically-trained scientists and scientifically-trained philosophers, who met on Thursdays, in ‘Red Vienna’, in the years after the First World War. They were trying to remould philosophy in a world turned upside down not just by war, but by major advances in science. Their hero was not Descartes or Hegel but Albert Einstein.

The group’s new doctrine rejected great swathes of earlier philosophy, from meditations on the existence of God to declarations on the nature of History, as utterly meaningless. When the Nazis took power, they fled to England and America, where their ideas put down new roots, and went on to have a profound impact.

Melvyn is joined by Barry Smith, Professor of Philosophy at the University of London; Nancy Cartwright, Professor of Philosophy at the London School of Economics; and Thomas Uebel, Professor of Philosophy at Manchester University.

In the introduction to Thomas Spratt’s History of the Royal Society, there is a poem about man called Francis Bacon which declares ‘Bacon, like Moses, led us forth at last, The barren wilderness he past, Did on the very border stand Of the blest promis’d land, And from the mountain’s top of his exalted wit, Saw it himself, and shew’d us it’.

Francis Bacon was a lawyer and political schemer who climbed the greasy pole of Jacobean politics and then fell down it again. But he is most famous for developing an idea of how science should be done – a method that he hoped would slough off the husk of ancient thinking and usher in a new age. It is called Baconian Method and it has influenced and inspired scientists from Bacon’s own time to the present day.

Melvyn Bragg and guests discuss an iconic piece of 20th century maths – Gödel’s Incompleteness Theorems. In 1900, in Paris, the International Congress of Mathematicians gathered in a mood of hope and fear. The edifice of maths was grand and ornate but its foundations, called axioms, had been shaken. They were deemed to be inconsistent and possibly paradoxical. At the conference, a young man called David Hilbert set out a plan to rebuild the foundations of maths – to make them consistent, all encompassing and without any hint of a paradox.

Hilbert was one of the greatest mathematicians that ever lived, but his plan failed spectacularly because of Kurt Gödel. Gödel proved that there were some problems in maths that were impossible to solve, that the bright clear plain of mathematics was in fact a labyrinth filled with potential paradox. In doing so Gödel changed the way we understand what mathematics is and the implications of his work in physics and philosophy take us to the very edge of what we can know.

With Marcus du Sautoy, Professor of Mathematics at Wadham College, University of Oxford; John Barrow, Professor of Mathematical Sciences at the University of Cambridge and Gresham Professor of Geometry and Philip Welch, Professor of Mathematical Logic at the University of Bristol.

Melvyn Bragg and guests discuss the strange mathematics of probability where heads or tails is a simple question with a far from simple answer.

Gambling may be as old as the hills but probability as a mathematical discipline is a relative youngster. Probability is the field of maths relating to random events and, although commonplace now, the idea that you can pluck a piece of maths from the tumbling of dice, the shuffling of cards or the odds in the local lottery is a relatively recent and powerful one. It may start with the toss of a coin but probability reaches into every area of the modern world, from the analysis of society to the decay of an atom.

With Marcus du Sautoy, Professor of Mathematics at the University of Oxford; Colva Roney-Dougal, Lecturer in Pure Mathematics at the University of St Andrews; Ian Stewart, Professor of Mathematics at the University of Warwick

Melvyn Bragg and guests discuss Newton’s Laws of Motion. In 1687 Isaac Newton attempted to explain the movements of everything in the universe, from a pea rolling on a plate to the position of the planets. It was a brilliant, vaultingly ambitious and fiendishly complex task; it took him three sentences.

These are the three laws of motion with which Newton founded the discipline of classical mechanics and conjoined a series of concepts – inertia, acceleration, force, momentum and mass – by which we still describe the movement of things today. Newton’s laws have been refined over the years – most famously by Einstein – but they were still good enough, 282 years after they were published, to put Neil Armstrong on the Moon.

With Simon Schaffer, Professor in History and Philosophy of Science at the University of Cambridge and Fellow of Darwin College; Raymond Flood, University Lecturer in Computing Studies and Mathematics and Senior Tutor at Kellogg College, University of Oxford; Rob Iliffe, Professor of Intellectual History and History of Science at the University of Sussex